2006 A/C High Speed Fan Problem

[jjemg]

I have a 2006 mini base cab and have a high speed fan issue that I hope someone has encountered and can point me right to the problem.
On all the newer systems that have come up in the last 20 years or more when you turn on the A/C inside the cabin the high speed fan will come on and stay on to pull air across the condenser. As it seems my daughters mini does this without issue. It's a 2003 but should not be any different. They are both Gen1 cars.
What is happening is after crank up the compressor will start and the fan begins a cycle of coming on when it reaches too high of a pressure (assuming that's the high pressure switch) It will run on high speed and drop the pressure down and then cycle off until the pressure gets to high again. This is repeated and is impossible to fine tune my target coolant amount and also increases the cabin air temp.
Has anyone had this problem?
This has to be easy. It's just something Im overlooking.
What I hope to achieve is push the A/C blue flake and the fan to work on high speed the entire time it's on without changing the original wiring.
Any help would be appreciated!
Jimmy